Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals → CMB
Abstract view

# Correction to a Theorem on Total Positivity

Published:2006-06-01
Printed: Jun 2006
• Carl Johan Ragnarsson
• Wesley Wai Suen
• David G. Wagner
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
 Format: HTML LaTeX MathJax PDF PostScript

## Abstract

A well-known theorem states that if $f(z)$ generates a PF$_r$ sequence then $1/f(-z)$ generates a PF$_r$ sequence. We give two counterexamples which show that this is not true, and give a correct version of the theorem. In the infinite limit the result is sound: if $f(z)$ generates a PF sequence then $1/f(-z)$ generates a PF sequence.
 Keywords: total positivity, Toeplitz matrix, Pólya frequency sequence, skew Schur function
 MSC Classifications: 15A48 - Positive matrices and their generalizations; cones of matrices15A45 - Miscellaneous inequalities involving matrices 15A57 - Other types of matrices (Hermitian, skew-Hermitian, etc.)05E05 - Symmetric functions and generalizations

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/